## Matrix Algebra: Binary Operations

Many university STEM major programs have reduced the credit hours for a course in Matrix Algebra or have simply dropped the course from their curriculum.   The content of Matrix Algebra in many cases is taught just in time where needed.  This approach can leave a student with many conceptual holes in the required knowledge of matrix algebra.

In this series of blogs, we bring to you ten topics that are of immediate and intermediate interest for Matrix Algebra.

Here is the third topic where we talk about binary operations of matrices – subtraction, addition, and multiplication.  Linear combination of matrices and rules of binary operations are discussed. Get all the resources in form of textbook content, lecture videos, multiple choice test, problem set, and PowerPoint presentation.

Binary Operations

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## Matrix Algebra: Introduction

Many university STEM major programs have reduced the credit hours for a course in Matrix Algebra or have simply dropped the course from their curriculum.   The content of Matrix Algebra in many cases is taught just in time where needed.  This approach can leave a student with many conceptual holes in the required knowledge of matrix algebra.

In this series of blogs, we bring to you ten topics that are of immediate and intermediate interest for Matrix Algebra.

Here is the first topic where we define a matrix, vector, submatrix, square matrix, triangular matrix (upper and lower), diagonal matrix, identity matrix, and diagonally dominant matrix.  Get the information in form of textbook content, lecture videos, multiple choice test, problem set and PowerPoint presentation.

Introduction

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• Holistic Numerical Methods Open Course Ware:
• the textbooks on
• the Massive Open Online Course (MOOCs) available at

## Reporting results from prior NSF support when PIs on a proposal were PIs on a recent grant

Most NSF proposals limit you to 15 pages for proposal description, and most of us mortals have a hard time fully communicating our idea within the limit.  So one would like to minimize reporting prior NSF support that is not related to the proposal or count the same prior results description toward several investigators if they have previously worked together on an NSF grant.

The clarification brought here is for reporting results from prior NSF support. Read the requirements here — https://www.nsf.gov/pubs/policydocs/pappg18_1/pappg_2.jsp#IIC2diii

The purpose of this section is to assist reviewers in assessing the quality of prior work conducted with prior or current NSF funding. If any PI or co-PI identified on the proposal has received prior NSF support including:

• an award with an end date in the past five years; or
• any current funding, including any no-cost extensions,

information on the award is required for each PI and co-PI, regardless of whether the support was directly related to the proposal or not. In cases where the PI or any co-PI has received more than one award (excluding amendments to existing awards), they need only report on the one award that is most closely related to the proposal. Support means salary support, as well as any other funding awarded by NSF, including research, Graduate Research Fellowship, Major Research Instrumentation, conference, equipment, travel, and center awards, etc.

For a proposal recently submitted, I was working with four Co-PIs — let’s call them B, C, D, and E. I will call myself A.

We had worked on a directly related NSF grant in 2013–16 period for which A was the PI, and B and C were Co-PIs. On talking to a NSF official, writing prior-support results description for this grant would only count toward the reporting by one of the three investigators, A, B, or C. So let’s consider it to be counted toward Co-PI B. If PI A or Co-PI C have had other NSF grants as a PI or Co-PI which are current or have been active within the past five years, you will need to report one each for A and C (you cannot game the system if PI A or Co-PI C does not have another grant to report on, while Co-PI B does; each PI or Co-PI has to write prior support description on one grant each, unless a PI or Co-PI has none to report – for an award with an end date in the past five years or any current funding, including any no-cost extensions).

As per the NSF official, you cannot count the same prior-support description for more than one PI/Co-PI.

I got additional advice from my fellow investigator  — if you have an unrelated grant that you need to report under prior support guidelines, do so at the end of the proposal description under the heading of “Other Non-Related Prior NSF-Supported Projects”. Otherwise, it will unnecessarily distract the reviewer.

## An FE Math Problem in Analytical Geometry

“The Fundamentals of Engineering (FE) exam is generally the first step in the process of becoming a professional licensed engineer (P.E.). It is designed for recent graduates and students who are close to finishing an undergraduate engineering degree from an EAC/ABET-accredited program” – FE Exam NCEES

For most engineering majors, mathematics is a required part of the examination. Here is a question from analytical geometry.

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• Holistic Numerical Methods Open Course Ware:
• the textbooks on
• the Massive Open Online Course (MOOCs) available at

## An FE Exam Math Problem in Partial Differential Calculus

“The Fundamentals of Engineering (FE) exam is generally the first step in the process of becoming a professional licensed engineer (P.E.). It is designed for recent graduates and students who are close to finishing an undergraduate engineering degree from an EAC/ABET-accredited program” – FE Exam NCEES

For most engineering majors, mathematics is a required part of the examination. Here is a question from differential calculus.

This post is brought to you by

• Holistic Numerical Methods Open Course Ware:
• the textbooks on
• the Massive Open Online Course (MOOCs) available at

## An FE Exam Math Problem in Ordinary Differential Equations

“The Fundamentals of Engineering (FE) exam is generally the first step in the process of becoming a professional licensed engineer (P.E.). It is designed for recent graduates and students who are close to finishing an undergraduate engineering degree from an EAC/ABET-accredited program” – FE Exam NCEES

For most engineering majors, mathematics is a required part of the examination. Here is a question from ordinary differential equations.

This post is brought to you by

• Holistic Numerical Methods Open Course Ware:
• the textbooks on
• the Massive Open Online Course (MOOCs) available at

## One Two, No Test Review

In Spring 2018 for the EML3041 Computational Methods course, I assigned students to write a nursery rhyme on numerical methods using the “one, two, buckle my shoe” prompt.  Here is a sample, and more will be shared in the next few weeks.

The students were given the choice of going anonymous, use only initials or their full name as the byline.  Some opted not to be published while others added the audio version as well.

One, Two
by Cedric Bellard

One, two,
No test review
Three, four,
Better study before
Five, six,
Taylor series will stick
Seven, eight,
You will differentiate
Nine, ten,
Must remember programming again
Eleven, twelve,
Hours you must delve
Thirteen, fourteen,
Mini-project must be clean
Fifteen, sixteen,
Frq is the routine
Seventeen, eighteen,
Never daydream
Nineteen, twenty,
You will learn plenty!